Dynamics in the Vicinity of the Stable Halo Orbits

Area of Science:

• Celestial Mechanics
• Astrodynamics
• Space Mission Design

Background:

• The Earth-Moon system is a key area for space exploration, with stable halo orbits offering unique dynamical properties.
• Understanding the vicinity of these halo orbits is crucial for designing efficient and stable trajectories for space missions.

Purpose of the Study:

• To compute and analyze orbits in the vicinity of stable halo orbits within the Earth-Moon system's circular restricted three-body problem.
• To explore a 3-parameter family of quasi-halo orbits, including partially elliptic and partially hyperbolic types, and their 3D invariant tori.
• To identify potential applications of these newly computed orbits for space missions.

Main Methods:

• Development of an algorithm to quantify the size of invariant surfaces for orbit characterization.
• Numerical computation and analysis of partially elliptic, partially hyperbolic, and elliptic quasi-halo orbits.
• Investigation of dynamical behavior, including stability bifurcations and nonlinear Jacobi constant variations.

Main Results:

• Identification of 2D quasi-periodic tori (partially elliptic/hyperbolic) and 3D quasi-periodic tori (elliptic orbits).
• Detection of a stability bifurcation where partially elliptic tori transition to partially hyperbolic.
• Observation of nonlinear Jacobi constant behavior distinct from orbits near unstable halo orbits.

Conclusions:

• The study reveals a complex dynamical structure in the vicinity of stable halo orbits, expanding the known family of solutions.
• The findings provide a comprehensive understanding of quasi-halo orbits and their characteristics, relevant for future space mission planning.
• The identified orbits and their properties offer valuable insights for optimizing trajectories and station-keeping in Earth-Moon space.